I am being denied unemployment for misconduct. Is giving out a birthdate a HIPAA violation? I don't know whether it's a HIPAA violation or not. I'm an employer, not a medical facility. I've not had any need to dive into that side of HIPAA and acquaint myself with all that additional complexity.
What I can tell you is that giving out ANY information on a patient for personal purposes is inappropriate and, I expect, a violation of your employer's work rules. If an employee of the medical facility asks for a patient's birthdate for legitimate purposes (whether a doctor, nurse, the billing department, etc.), that's appropriate. If someone asks for patient information (including a birthdate) for any other reason, it would be entirely inappropriate for you to comply. I expect there's a reason why you've never said who you gave the birthdate to and why.
Then why are stores allowed to ask to see a drivers license to cash a check, which has your birthdate on it? Because they're asking YOU for YOUR information. You are free to comply or not comply as you see fit. A medical provider is a third party and governed by onerous patient confidentiality regulations. Do you want your doctor's office giving out whatever information they feel like to whomever without your authorization?
Also, what information is my former employer allowed to give out if someone call for a reference for a job? Anything they wish to provided it's truthful and represents their honest opinion. If you're wondering if they can tell other employers that you were terminated and why, the answer is yes.